Question

Sales of People magazine are compared over a 5-week period at four Borders outlets in Chicago.

Weekly Sales
Store 1	Store 2	Store 3	Store 4
103	98	89	105
104	77	94	117
105	83	75	86
112	82	104	104
114	98	91	98

Fill in the missing data. (Round your p-value to 4 decimal places, mean values to 1 decimal place, and other answers to 3 decimal places.)

Treatment	Mean	n	Std. Dev
Store 1
Store 2
Store 3
Store 4
Total

One-Factor ANOVA
Source	SS	df	MS	F	p-value
Treatment
Error
Total

(a)	Based on the given hypotheses choose the correct option.
	H0: μ1 = μ2 = μ3 = μ4
	H1: Not all the means are equal
	α = 0.05
	Reject the null hypothesis if F < 3.24 Reject the null hypothesis if F > 3.24

(b)	Determine the value of F. (Round your answer to 2 decimal places.)

F-value

(c)	On the basis of the above-determined values, choose the correct decision from below.
	Reject the null hypothesis. Fail to reject the null hypothesis.

(d)	Determine the p-value. (Round your answer to 4 decimal places.)

p-value

Answer 1

For the given samples the description of the sample is done in excel tool and some formulas are shown in that as:

Mean =AVERAGE(B2:B6) ,Standard deviation==STDEV.S(B2:B6)	Store 1	Store 2	Store 3	Store 4	Total
	103	98	89	105
	104	77	94	117
	105	83	75	86
	112	82	104	104
	114	98	91	98
Mean=	107.6	87.6	90.6	102	387.8
n= Sample size=	5	5	5	5	20
Standard deviation=	5.030	9.762	10.455	11.292	36.538

a) Performing one-factor ANOVA on the given samples in excel results is:

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Store 1	5	538	107.6	25.3
Store 2	5	438	87.6	95.3
Store 3	5	453	90.6	109.3
Store 4	5	510	102	127.5
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1333.35	3	444.45	4.9743	0.0126	3.2389
Within Groups	1429.6	16	89.35
Total	2762.95	19

a) Based on the Hypotheses:

H₀: μ₁ = μ₂ = μ₃ = μ₄

H₁: Not all the means are equal

Rejection region:

At 0.05 level of significance the F-critical value is 3.24 ( As computed in excel or can also be computed using F-table) so, Reject the null hypothesis if F > 3.24.

b) From the One way, ANOVA shown above the F statistic is calculated as:

F=4.97

c) Decision:

On the basis of the above F statistic and calculation, we reject the Null hypothesis since F >F-critical value=3.24.

d) P-value:

The P-value is computed using the excel tool as shown above through ANOVA as:

P-value=0.0126.